A flow facility to create a plane shear layer from a laminar and a turbulent boundary layer was established. The spread rate parameter for these two conditions was accurately determined. A four percent (maximum), nonturbulent disturbance level exists in the laminar boundary layer

Foss, J. F.

English

NASA Technical Reports Server

Final Report
NASA Langley Research Center
NGR 23-004-089
PRELIMINARY RESULTS FROM AN EXPERIMENTAL INVESTIGATION
OF THE INITIAL CONDITION EFFECTS ON A TURBULENT SHEAR LAYER
(NASA-CR-142072) PRELIMINARY RESULTS FROM N75-16764
AN EXPERIMENTAL INVESTIGATION OF THE INITIAL
CONDITION EFFECTS ON A TURBULENT SHEAR LAYER
Final Report (Michigan State Univ.) 21 p HC Unclas
$3.25 CSCL 20D G3/34 08985
prepared by
John F. Foss, Principal Investigator
Division of Engineering Research
MICHIGAN STATE UNIVERSITY
East Lansing, Michigan 48823
January 31, 1975
https://ntrs.nasa.gov/search.jsp?R=19750008692 2020-03-23T01:11:44+00:00Z
1. INTRODUCTION
The purpose of this report is to communicate the partial results
obtained to date in our investigation of the title problem. These studies
are continuing, and a complete documentation, including a discussion of
the relevant literature, will be provided in the future. The present
communication will satisfy the requirements of the original grant, how-
ever, and will allow it to be terminated.
Since a more complete documentation of the facility, procedures,
and results will be forthcoming and since certain alterations and improve-
ments will be affected in these matters, the current results will be pre-
sented with minimum discussion. However, it should be noted that the
findings to date are considered to add significant information to the
extant knowledge concerning initial condition effects on the development
of plane shear layers.
1.1. Experimental Facility
A central characteristic of the study was to examine the asymptotic
states of the shear layer created from the laminar and turbulent boundary
layer states on essentially the same flow system; that is, if the two
boundary layer states are achieved with only minor alterations, then
any influence of the overall geometric features of the flow field and/or
the probe and traverse system will be eliminated. This proved rather
more difficult than was anticipated, and numerous geometries were
examined. The flow system finally selected is shown in Figure 1. The
flow in the indicated contraction is from a 100 x 152 cm plenum chamber
fed by a one percent feedback speed controlled fan and is 10 x 100 cm at
the exit to the atmosphere. A laminar boundary layer exists at the end
of the 25.4 cm plate when a portion of the streaming flow is bled into the
small plenum chamber over the gap. Conversely, when the bleed flow is
eliminated, a turbulent boundary layer is established at the end of the
plate. The shear layer is the upper edge of the 10 x 100 cm wall jet;
the flow is bounded on the other three sides.
A computer -controlled stepping motor was used to traverse
the single (Disa gold) hot-wire probe utilized for the boundary layer and
shear layer velocity traverses. A T.I. 960A minicomputer was used to
process the hot-wire signals. The input voltage was digitized, and its
1
statistical character was interpreted using a 0. 5 fps increment calibra-
tion table. That is, the linearized hot-wire voltage E was processed to
store 30-second averages of E and E2. The combination of these values
allowed u and 62 to be obtained. (Note: For < V > = i'i + jv.+ kr, the
2
approximation was made that the single-wire data results in _ and uZ
This approximation is subject to the usual restrictions of V << i and
vr /u , Tv/u << 1.)
1.2. Experimental Results
The laminar and the turbulent boundary. layer velocity profiles
are shown in Figure 2. The difference in their physical extent is clearly
shown in Figure 2a, and the agreement of the laminar profile with the
Blasius solution is shown in Figure 2b. During the acquisition of the
data, the scope traces suggested that a heaving motion existed in the
laminar layer. That is, the fluctuation level at a point was nonzero,
but it was apparently caused by nonvortical or wave-like fluctuations.
The turbulent fluctuations were as expected. The velocity fluctuation
intensities presented in Figure 3 confirmed this. A simple analysis
(wherein the laminar boundary layer profile was assumed to maintain
its shape, but with a time varying thickness, 6(t), such that the displace-
ment of any segment of the layer was linearly proportional to its height)
was used to compute the fluctuation intensities. The parameter K was
arbitrarily selected to provide rough agreement at the midpoint of the
velocity profile. The agreement between the resulting analytical form
S1/2
Au = KF" [ ,] (1)
m
and the observed i values suggests that the physical processes are
similar to those described by this model.
However, it was also observed that the upper plenum served as
a Helmholtz resonator, and concentrated fluctuations at 70 hz and 80 hz
were observed in the boundary layer spectra for the turbulent and laminar
boundary layers respectively. The resonator frequencies are not con-
sidered to be dynamically significant. Specifically, the spectra at
x = 2. 54 cm show that the fluctuations in the naturally developing shear
layers either swamp the single frequency fluctuation (turbulent case) or
are far removed from it (=800 hz) for the laminar boundary layer. It
2
is pertinent to note that the Strouhal number for the laminar case is far
below that which is observed in natural transitions in shear layer studies.
(This point will be examined more completely in the final report.)
The normalized shear layer mean velocity data for x = 46, 56,
and 66 cm are presented in Figure 4, and the numerical data are presented
in Tables 1 and 2 for quantitative reference. The similarity parameter
was established by plotting u/um versus y -y () , where the latter is the
relative distance from the "centerline" of the velocity field. The y()
distributions were essentially the same for the two conditions and are
documented in the tables. The apparent origins, x o , of the shear layer
were then established by linear extrapolations of the u/um data from the
three x locations such that u/um = constant for [y -y(- )]/[x-x ]. For
the laminar and turbulent boundary layer cases, xo was -1.5 and 2. 5 cm,
respectively.
The choice of probability coordinates for the normalized data
was in response to the interest in the spread rate parameter o. The
following analysis relates a of the error function description (aflow) to
the standard deviation (prob ) of a Gaussian process distribution.
The cumulative distribution function for a Gaussian process is
F(a) '= [2 21 exp -( ) ] d (2)27.dr 2 (p
P P
and the error function form of the mean velocity distribution is
) { 1 + erf f y* } . (3)
m
The error function is defined as
erf (x) = t dt . (4)
In order to force (2) to be of the form shown in (3), the distribution F is
rewritten as
F(a ) = 0.5 + ~1- 2 " exp (- ) d (5)
p o p
where M = 0 is considered since y = 0. Note that the integral in (5) is of
the form of an error function. Let /(&2p ) = t and d = N2a( dt. Using
the definition of erf (x) given by (4), rewrite F(a ) as
3
F(a) = { 1+ erf a } . (6)
Comparing (3) and (6) and noting that a is the value of r/(T a- p) at the
point of interest, we obtain
p
or
f = . (7)
P
The "best fit" curves for the experimental data are presented in
Figure 5. The aflow values are essentially the same for the laminar and
for the turbulent boundary layer cases, but are markedly different from
the 'flow = 12 value commonly accepted for shear layers generated from
a laminar boundary layer. The difference between these results and
those of earlier studies may be in the disturbance level of the present
laminar layer; this effect is under investigation. Also, it is significant
that the error function satisfactorily describes the shear layer only for
u/um < 0.7. This feature, as well as the evaluation of cflow' are con-
sidered to be best revealed by the use of probability coordinates.
In addition to a further examination of the laminar boundary layer
disturbances at x = 0, the developing shear layer profiles and conditionally
sampled data to search for the coherent structures observed by other
investigators are considered to be important extensions of the present
studies.
1.3. Summary
A flow facility to create a plane shear layer from a laminar and
a turbulent boundary layer has been established. The spread rate para-
meter, aflow' for these two conditions has been accurately determined.
It is Oflow = 9.3 for the laminar boundary layer case, and Yflow = 9.5
for the turbulent boundary layer case. A four percent (maximum), non-
turbulent disturbance level exists in the laminar boundary layer. Further
experiments are underway to determine the significance of this distur-
bance level on the asymptotic shear layer.
The commonly used error function, in which Tflow appears, pro-
vides a good representation of u/u for 0 Su/u m  0. 7. Systematic
deviations from the error function are observed for fU/u 0. 7.max
4
yexhaust
20
PS
1.27
-I 0. 95
10
1 0 rounded 
"" -
90
T. I. 960A T. S. I.
H. W. A.
Figure 1. Schematic representation of the experimental facility.
(all dimensions in c.m.)
1. 78-
1.52
1.27-
1.01
0.51
I-
0.5-
t .
0. 5 1.0
BL
Figure Za. Boundary layer velocity velocity profiles -
dimensional representation.
6
4
.F
.
• " i " / d • , - ;P!..,.,M -N F! BI_ .,..L _ ! i t
laminar turbulent
3 - 6
2 4
/ d
1 2
lasius
solution
S + I u/un
0.5 1.0
X F 'ienA' i , L 1 I_. /7/
Figure 2b. Non-dimensional representation.
7
6 T
(t) (t + At)
laminar
o turbulent 2
- = K F" _
u
o m
o oo
0
oo/5a o
00
0
0
0
24 0
0
0
a o
o
0
a 0Sosolution
o
a e
o
g 0
K =0. 0163 00
0.05 u'/u m  0. 10
Figure 3a. Mean square fluctuation intensities for the laminar and
turbulent boundary layers and the near field shear layers.
Note: See equation (1) for the theoretical solution of & in
the unsteady laminar boundary layer.
8
Spectra to characterize the
boundary layer, y location e --
at u/u = 0. 5 e(f)
m
Note: u/6 -- 1. 2 x 104 laminar
S960 turbulent
0 500 hz
Figure 3b. Spectral content of the laminar boundary
layer fluctuations (arbitrary ordinate).
e (f)
0 500 hz
Figure 3c. Spectral content of the turbulent boundary
layer fluctuations (arbitrary ordinate).
e (f)
hz
500 1000
Figure 3d. x=l, y= -0. 02 (in.) Laminar B. L. Case
Spectral distributions in the
shear layer.
Note: N ,.
e 2 (f) - arbitrary units
e (f)
hz
500 1000
Figure 3e. x=l, y=-O.02 (in.) Turbulent B.L. Case.
10
symbol x(cm) x/O
* 46 2000
0 56 2440
66 2880
0. 15
0.10 -
0.05- 
0 0 0
0
00
-0.10- 
-0. 15-
0. 01 0. 1 0.3 0. 5 0. 7 0. 9 0 99
a.) U/Um vs. y* probability coordinates, Laminar B. L. Case
Figure 4. Normalized shear layer mean velocity profiles.
symbol x(cm) x/O
* 46 287
* 56 351
a 66 416
0. 15-
0. 5-
y*
0 -
-0.0 5-
-0. 1 - "A
-0. 15-
I I i I I l I ! I I I
0.01 0. 1 0.3 0. 5 0.7 0.9 0.99
Figure 4b. u/un vs. y* on probability coordinates, Turbulent Boundary Layer Case
turbulent B. L. case
o.... laminar B.L. case
---- flow 9.4
flow
-- = 12. 0flow
0. 15-
0. 10-
0.05-
y
S0
-0. 05--*
-0. 10-
* **
-0.15-
I I I I III I I I I
0.01 0. 1 0.3 0.5 0.7 0.9 0.99
Figure 5. u/u m vs. y*, probability coordinates, composite plot.
0. 15-
0. 10-
0. o5-
uyu
UI/ m
0. 10 0. 20
-0. 05-
-0. 10-
-0. 15- / u/U VS. y*'
Turbulent B. L. Case
Figure 6. Characteristic turbulence intensity data.
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Preliminary results from an experimental investigation of the initial condition effects on a turbulent shear layer

Abstract

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